It is often desirable to capture images of a planar test chart containing patterns designed for the measurement of characteristics of the imaging system. For many purposes, the ideal configuration is to have the test chart oriented perpendicular to the optical axis of the imaging system. In practice, attaining such ideal alignment, or measuring deviations from the ideal alignment in an existing setup, can be achieved only to a certain accuracy, which imposes limits on the accuracy of the characteristics intended to be measured by the chart. In view of these non-ideal alignment issues, testing is a three-dimensional (3D) problem rather than a relatively simpler two-dimensional (2D) problem.
The problem of measuring the position and orientation of an object in three dimensions from two-dimensional images is well known and many methods have been developed in an effort to address this. While the position of visible features in two dimensions is well defined by images, removing ambiguities in the position along the third dimension is difficult.
Previous methods generally rely on one or more of the following techniques:
(i) imaging three dimensional objects or scenes of a known geometry, to provide reference points in known relative positions to one another in three dimensions;
(ii) imaging an object or scene from multiple spatial locations in order to use the phenomenon of stereo vision to remove ambiguities in the location of features in the third dimension;
(iii) imaging planar objects or planar portions of three dimensional objects where the planes are oriented at large angles away from being perpendicular to the optical axis of the imaging system, in order that the perspective projection distortion dominates over optical distortions of the imaging system.
These techniques are unsuitable for use in the case when the object to be imaged is necessarily planar and oriented close to perpendicular to the optical axis. This requirement occurs in cases such as an optical device manufacturing process where the imaging quality of many products must be tested rapidly.
Methods for measuring the 3D geometric parameters of an imaging system using a single photograph from a planar target rely on the detection of features on the object such as corners or dots in the image of the object. Such features can be detected and located to an accuracy of the order of one tenth of a pixel on the imaging sensor. This is not adequate to calculate the geometric parameters of the system to the accuracy that is required for certain system performance measurements. To partially compensate for the limited spatial resolution of feature detection, many such features are often used, covering much of the surface area of the object, although this still results in limited accuracy in the derived geometric parameters.